Smoke can be seen billowing across the city due to the fire in the Wakefield Road area.
Wakefield Road and Ossett bypass have been closed with people being urged to avoid the area.
Wakefield Council tweeted reports of the blaze, asking people in the area to stay safe due to the increasing amount of smoke.
Witnesses say the smoke can be seen from as far as Huddersfield.
West Yorkshire Fire and Rescue Service (WYFRS) said that multiple vehicles and tyres were involved in the fire.
Ten pumps have been sent to the scene to tackle the blaze, including crews from Ossett, Wakefield, Pontefract, Normanton, Hunslet and Dewsbury.
A spokeswoman from WYFRS said: "We were called at 2.45pm to reports of a fire at a scrapyard on Wakefield Road in Ossett.
"Eight crews are currently at the scene, along with three support pumps.
"No casualties are reported."
*Updates as we get them.